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131.
Input data modeling is a critical component of a successful simulation application. A perspective of the area is given with an emphasis on available probability distributions as models, estimation methods, model selection and discrimination, and goodness of fit. Three specific distribution classes (lambda,S
B
, TES processes) are discussed in some detail to illustrate characteristics that favor input models. Regarding estimation, we argue for maximum likelihood estimation over method of moments and other matching schemes due to intrinsic superior properties (presuming a specific model) and the capability of accommodating messy data types. We conclude with a list of specific research problems and areas warranting additional attention. 相似文献
132.
Ladislav Adamec 《Journal of Mathematical Analysis and Applications》2005,304(2):504-510
We present a new proof of the Liouville formula for a d-dimensional linear dynamic system xΔ=A(t)x on a time scale T, where T is in a sense small. Our proof demonstrates that Liouville's formula on small time scales is a direct consequence of its well-known counterpart for ordinary differential equations. 相似文献
133.
We study a new nonlocal approach to the mathematical modelling of the chemotaxis problem, which describes the random motion of a certain population due to a substance concentration. Considering the initial–boundary value problem for the fractional hyperbolic Keller–Segel model, we prove the solvability of the problem. The solvability result relies mostly on fractional calculus and kinetic formulation of scalar conservation laws. 相似文献
134.
C. Miehe M. Lambrecht E. Gürses 《Journal of the mechanics and physics of solids》2004,52(12):2725-2769
We propose an approach to the definition and analysis of material instabilities in rate-independent standard dissipative solids at finite strains based on finite-step-sized incremental energy minimization principles. The point of departure is a recently developed constitutive minimization principle for standard dissipative materials that optimizes a generalized incremental work function with respect to the internal variables. In an incremental setting at finite time steps this variational problem defines a quasi-hyperelastic stress potential. The existence of this potential allows to be recast a typical incremental boundary-value problem of quasi-static inelasticity into a principle of minimum incremental energy for standard dissipative solids. Mathematical existence theorems for sufficiently regular minimizers then induce a definition of the material stability of the inelastic material response in terms of the sequentially weakly lower semicontinuity of the incremental variational functional. As a consequence, the incremental material stability of standard dissipative solids may be defined in terms of the quasi-convexity or the rank-one convexity of the incremental stress potential. This global definition includes the classical local Hadamard condition but is more general. Furthermore, the variational setting opens up the possibility to analyze the post-critical development of deformation microstructures in non-stable inelastic materials based on energy relaxation methods. We outline minimization principles of quasi- and rank-one convexifications of incremental non-convex stress potentials for standard dissipative solids. The general concepts are applied to the analysis of evolving deformation microstructures in single-slip plasticity. For this canonical model problem, we outline details of the constitutive variational formulation and develop numerical and semi-analytical solution methods for a first-level rank-one convexification. A set of representative numerical investigations analyze the development of deformation microstructures in the form of rank-one laminates in single slip plasticity for homogeneous macro-deformation modes as well as inhomogeneous macroscopic boundary-value problems. The well-posedness of the relaxed variational formulation is indicated by an independence of typical finite element solutions on the mesh-size. 相似文献
135.
136.
Plane surface suddenly set in motion in a viscoelastic fluid with fractional Maxwell model 总被引:6,自引:0,他引:6
The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced. The flow near
a wall suddenly set in motion is studied for a non-Newtonian viscoelastic fluid with the fractional Maxwell model. Exact solutions
of velocity and stress are obtained by using the discrete inverse Laplace transform of the sequential fractional derivatives.
It is found that the effect of the fractional orders in the constitutive relationship on the flow field is significant. The
results show that for small times there are appreciable viscoelastic effects on the shear stress at the plate, for large times
the viscoelastic effects become weak.
The project supported by the National Natural Science Foundation of China (10002003), Foundation for University Key Teacher
by the Ministry of Education, Research Fund for the Doctoral Program of Higher Education 相似文献
137.
138.
Courtney Nagle Tyler Tracy Gregory Adams Daniel Scutella 《International Journal of Mathematical Education in Science & Technology》2017,48(4):573-586
This paper investigates outcomes of building students’ intuitive understanding of a limit as a function's predicted value by examining introductory calculus students’ conceptions of limit both before and after instruction. Students’ responses suggest that while this approach is successful at reducing the common limit equals function value misconception of a limit, new misconceptions emerged in students’ responses. Analysis of students’ reasoning indicates a lack of covariational reasoning that coordinates changes in both x and y may be at the root of the emerging limit reached near x = c misconception. These results suggest that although dynamic interpretations of limit may be intuitive for many students, care must be taken to foster a dynamic conception that is both useful at the introductory calculus level and is in line with the formal notion of limit learned in advanced mathematics. In light of the findings, suggestions for adapting the pedagogical approach used in this study are provided. 相似文献
139.
Farzad Radmehr Michael Drake 《International Journal of Mathematical Education in Science & Technology》2017,48(7):1043-1071
Several studies have explored students’ understanding of the relationships between definite integrals and areas under curve(s). So far, however, there has been less attention to students’ understanding of the Fundamental Theorem of Calculus (FTC). In addition, students’ metacognitive experiences and skills whilst solving FTC questions have not previously been explored. This paper explored students’ mathematical performance, metacognitive experiences and metacognitive skills in relation to FTC questions by interviewing nine university and eight Year 13 students. The findings show that several students had difficulty solving questions related to the FTC and that students’ metacognitive experiences and skills could be further developed. 相似文献
140.
Malliavin calculus is implemented in the context of Hairer (2014) [16]. This involves some constructions of independent interest, notably an extension of the structure which accommodates a robust, and purely deterministic, translation operator, in -directions, between “models”. In the concrete context of the generalized parabolic Anderson model in 2D – one of the singular SPDEs discussed in the afore-mentioned article – we establish existence of a density at positive times. 相似文献